안녕하세요. 학생 답변이 좀 늦어 미안합니다. 전체 실라부스를 아래와 같이 공개합니다.

각 파트에 내용을 살펴보시고 수업 내용을 파악하시기 바랍니다. (조금 내용이 길수 있습니다.)

 

먼저 New IB Math Core topic Series는 다음과 같이 구성되어 있습니다.

 

1. STRAIGHT LINES

Core. 1.1 The equation of a straight line

Core. 1.2 Parallel and perpendicular lines

 

 

2. SOLVING EQUATIONS

Core. 2.1 Factored form

Core. 2.2 Quadratic equations

Core. 2.3 End behavior of polynomial graph

Core. 2.4 Solving polynomial equations using technology

Core. 2.5 Solving other equations using technology

 

 

3. QUADRATIC FUNCTIONS

Core. 3.1 Quadratic functions

Core. 3.2 Graphs of quadratic functions

Core. 3.3 Using the discriminant

Core. 3.4 Problem solving with quadratics

Core. 3.5 Quadratic inequalities

 

 

4. FUNCTIONS

Core. 4.1 Relations and functions

Core. 4.2 Function notation

Core. 4.3 Domain and range

Core. 4.4 Rational functions

Core. 4.5 Composite functions

Core. 4.6 Inverse functions

 

 

5. TRANSFORMATIONS OF FUNCTIONS

Core. 5.1 Translations

Core. 5.2 Stretches

Core. 5.3 Reflections

Core. 5.4 Miscellaneous transformations

Core. 5.5 The graph of y=​1/f(x)​​

6. SURDS AND EXPONENTS

Core. 6.1 Scientific notation

Core. 6.2 Exponents

Core. 6.3 Surds and other radicals

Core. 6.4 Laws of exponents

 

 

7. SEQUENCES AND SERIES

Core. 7.1 Number sequences

Core. 7.2 Arithmetic sequences

Core. 7.3. Series and sigma notation

Core. 7.4 Arithmetic series

Core. 7.5 Geometric sequences

Core. 7.6 Finite geometric series

Core. 7.7 Infinite geometric series

Core. 7.8 Growth and decay

Core. 7.9 Financial mathematics

 

 

8. MEASUREMENT

Core. 8.1 Perimeter and area formulae

Core. 8.2 Surface area

Core. 8.3 Volume

Core. 8.4 Bearings

 

 

9. RIGHT ANGLED TRIANGLE TRIGONOMETRY

Core. 9.1 Right angles trigonometric ratios

Core. 9.2 The Pythagorean identity

Core. 9.3 Radian measure

Core. 9.4 Arc length and sector area

Core. 9.5 The unit circle

Core. 9.6 Multiples of ​​π/6​​ and ​​π/4​​

Core. 9.7 Finding angles

Core. 9.8 Inverse trigonometric ratios

Core. 9.9 Right angles in geometric figures

 

 

10. NON-RIGHT ANGLED TRIANGLE TRIGONOMETRY

Core. 10.1 The area of a triangle

Core. 10.2 The sine rule

Core. 10.3 The cosine rule

 

 

11. POINTS IN SPACE

Core. 11.1 Points in space

Core. 11.2 Measurement

 

 

12. TRIGONOMETRIC FUNCTIONS

Core. 12.1 Periodic behaviour

Core. 12.2 The sine and cosine functions

Core. 12.3 Basic trigonometric functions

Core. 12.4 Modelling periodic behaviour

Core. 12.5 Trigonometric equations

 

 

13. SETS AND VENN DIAGRAMS

Core. 13.1 Sets

Core. 13.2 Intersection and union

Core. 13.3 Venn diagrams

Core. 13.4 Problem solving with Venn diagrams

 

 

14. PROBABILITY

Core. 14.1 Theoretical probability

Core. 14.2 The addition law of probability

Core. 14.3 Conditional probability

Core. 14.4 Independent events

Core. 14.5 Bayes' theorem

 

 

 

 

 

 

15. SAMPLING AND DATA

Core. 15.1 Data collection and Errors in sampling

Core. 15.2 Sampling methods

Core. 15.3 Writing surveys

Core. 15.4 Types of data

Core. 15.5 Simple and grouped discrete data

Core. 15.6 Continuous data

 

 

16. STATISTICS

Core. 16.1 Measuring the centre of data

Core. 16.1 Choosing the appropriate measure

Core. 16.2 Using frequency tables & Grouped data

Core. 16.3 Measuring the spread of data

Core. 16.4 Box and whisker diagrams (Parallel box and whisker diagrams)

Core. 16.5 Outliers

Core. 16.7 Cumulative frequency graphs

Core. 16.8 Variance and standard deviation

 

 

다음 New IB Math AA Common topics는 다음과 같이 구성되어 있습니다.

1. THE BINOMIAL THEOREM

AA1.1 Factorial notation, Permutation and Binomial Coefficient

AA1.2 Binomial expansions and the binomial theorem

 

2. FUNCTIONS

AA2.1 Sign diagrams

AA2.2 Rational functions

AA2.3 Inverse functions

AA2.4 Graphs of functions

AA2.5 Absolute value functions

 

3. EXPONENTIAL FUNCTIONS

AA3.1 Exponential functions

AA3.2 Exponential equations

AA3.3 Growth and decay

[REVIEW] Growth and Decay including Compound interest

 

4. LOGARITHMS

AA4.1 Logarithmic Definition

AA4.2 Laws of logarithms and The change of base rule

AA4.3 Solving exponential equations using logarithms

AA4.4 Logarithmic functions

 

5. TRIGONOMETRIC EQUATIONS AND IDENTITIES

AA5.1 Trigonometric identities

AA5.2 Double angle identities

AA5.3 Trigonometric equations

 

6. INTRODUCTION TO DIFFERENTIATION

AA6.1 Limits

AA6.2 Rates of change and Instantaneous rates of change

AA6.3 Differentiation from first principles

 

 

 

7. RULES OF DIFFERENTIATION

AA7.1 Simple rules of differentiation

AA7.2 The product rule and The quotient rule

AA7.3 The chain rule

AA7.4 Derivatives of exponential functions and logarithmic functions

AA7.5 Derivatives of trigonometric functions

 

8. PROPERTIES OF CURVES

AA8.1 Tangents and Normals

AA8.2 Increasing and decreasing, Stationary points, Shape and Inflection points

(Understanding functions and their derivatives)

 

9. APPLICATIONS OF DIFFERENTIATION

AA9.1 Rates of change

AA9.2 Optimisation

 

10. INTRODUCTION TO INTEGRATION

AA10.1 Antidifferentiation, Approximating the area under a curve and The Riemann integral

AA10.2 The Fundamental Theorem of Calculus

 

11. TECHNIQUES FOR INTEGRATION

AA11.1 Rules for integration

AA11.2 Integrating and Integration by substitution

 

12. DEFINITE INTEGRALS

AA12.1 Definite integrals

AA12.2 The area above a curve and The area under a curve

AA12.3 The area between two functions

 

13. KINEMATICS

AA13.1 Displacement, Velocity and Acceleration

AA13.2 Speed

 

14. BIVARIATE STATISTICS

AA14.1 Association between numerical variables

AA14.2 Pearson's product-moment correlation coefficient

AA14.3 The coefficient of determination

AA14.4 Line of best fit, Least squares regression line and The regression line of against

15. DISCRETE RANDOM VARIABLES

AA15.1 Random variables, Discrete probability distributions, Expectation

AA15.2 The binomial distribution

AA15.3 Poisson distribution

 

16. THE NORMAL DISTRIBUTION

AA16.1 Definition of the normal distribution, Calculating probabilities and Quantiles

AA16.2 The standard normal distribution

 

 

마지막으로 New IB Math AA HL Only Series는 다음과 같이 구성되어 있습니다.

1. FURTHER TRIGONOMRTRY

AAHL 1.1 Reciprocal trigonometric functions

AAHL 1.2 Inverse trigonometric functions

AAHL 1.3 Compound angle identities

  

2. INTRODUCTION TO COMPLEX NUMBERS

AAHL 2.1 Definition of complex numbers

AAHL 2.2 Operations with complex numbers

  

3. REAL POLYNOMIALS

AAHL 3.1 Polynomial division, The Remainder theorem and The Factor theorem

AAHL 3.2 The Fundamental Theorem of Algebra

AAHL 3.3 Sum and product of roots theorem

  

4. COMPLEX NUMBERS

AAHL 4.1 The complex plane

AAHL 4.2 Polar form and Euler's form

AAHL 4.3 De Moivre's theorem

AAHL 4.4 Nth Roots Method

  

5. FURTHER FUNCTIONS

AAHL 5.1 Even and odd functions

AAHL 5.2 The graph of

AAHL 5.3 Absolute value functions

AAHL 5.4 Rational functions and Partial fractions

 

6. COUNTING PRINCIPLE AND FURTHER BINOMIAL THEOREM

AAHL 6.1 The binomial theorem for

AAHL 6.2 The binomial theorem for

  

7. REASONING AND PROOF

AAHL 7.1 Proof by deduction, Disproof by counter example and

AAHL 7.2 Proof by contrapositive, Proof by contradiction: reductio ad absurdum

  

8. PROOF BY MATHEMATICAL INDUCTION

AAHL 8.1 The process of induction

AAHL 8.2 The principle of mathematical induction

  

9. VECTORS

AAHL 9.1 Vectors and Geometric Operations

AAHL 9.2 Vectors in the plane or the space

AAHL 9.3 The scalar product of two vectors

AAHL 9.4 The vector product of two vectors

  

10. VECTOR APPLICATIONS

AAHL 10.1 The vector equation of the line on 3D

AAHL 10.2 The angle between two lines

AAHL 10.3 Constant velocity problems

AAHL 10.4 The shortest distance from a line to a point

AAHL 10.5 Vector equation of plane

AAHL 10.6 Row Reduction of Relevant Matrix

AAHL 10.7 The shortest distance from a plane to a point

  

11. LIMITS

AAHL 11.1 The existence of limits

AAHL 11.2 Trigonometric limits

AAHL 11.3 Continuity

  

12. FURTHER DIFFERENTIAL CALCULUS

AAHL 12.1 Basic Differentiation Total Review

AAHL 12.2 Differentiability and continuity

AAHL 12.3 Implicit differentiation

AAHL 12.4 Derivatives of inverse trigonometric functions

AAHL 12.5 L'ôpital's rule

AAHL 12.6 Rates of change, Optimisation and Related rates

  

13. FURTHER INTEGRATION

AAHL 13.1 Basic Integration Total Review : Rules for integration, Integrating and Integration by substitution

AAHL 13.2 Integration by parts

AAHL 13.3 Definite integrals Total Review

AAHL 13.4 The area between two functions And Solids of revolution

AAHL 13.5 Improper integrals

AAHL 13.6 Kinematics

  

14. TAYLOR AND MACLAURIN SERIES

AAHL 14.1 Definition of Taylor and Maclaurin Series

AAHL 14.2 Transformations of Taylor and Maclaurin Series

 

15. DIFFERNTIAL EQUATIONS

AAHL 15.1 Euler's Method

AAHL 15.2 Differential Equation: Separable differential Equation

AAHL 15.3 Differential Equation: Homogeneous differential Equation

AAHL 15.4 Differential Equation: The integration factor method

 

 

 

AAHL 15.5 Logistic growth

 

차후 강의 선택시 참고하시기를 바랍니다.